Question

if f(x)isdivided by (x+9) then the reminder is​

Answer 1

Answer:

The remainder is f(-9)

Explanation:

According to remainder theorem, If p(x) is divided by ( x + a ), then the remainder will be p(-a).

here, 9 corresponds with a, So, the remainder will be f(-9).

Why remainder theorem is true?

Let's suppose p(x) is divided by ( x + a) then we will get ( x + a ) ( b) + remainder

here, -a is the zero of ( x + a), So, if we take p(-a), we will get:

= ( - a + a )(b) + remainder

= 0×b + remainder

= remainder !

We could restate it as : If p(x) is divided by (x + a), then the remainder is p(b), where b is the zero of (x + a).

Note: Factor theorem and remainder theorem are the same thing, Factor theorem is just a special case where the remainder is zero.